For a set of predictions, we have the following constraints \(P\ge 0\) , \(N\ge 0\) , \(|S^p|+|S^n| > 0\) , \(\beta \ge 0\)  and \(\gamma > 0\) . We can decrease the calibration error by either reducing \(\alpha \)  and/or increasing \(r\) . [1]} have shown that their refinement based approach improves calibration however, they do not provide the reasoning behind such an observation. Their observation can now be supported by the relationship described in Equation (REF ).
